Econometrica: May 1995, Volume 63, Issue 3

The Normal Approximation for Semiparametric Averaged Derivatives

https://doi.org/0012-9682(199505)63:3<667:TNAFSA>2.0.CO;2-0
p. 667-680

P. M. Robinson

With the same normalization as that for standard parametric statistics, and centered at a parameter of interest, many semiparametric estimates based on $n$ observations have been shown to be root-$n$-consistent and asymptotically normal. In the context of semiparametric averaged derivative estimates, we go further by showing that the rate of convergence of the finite-sample distribution to the normal limit distribution can equal that of standard parametric statistics.

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